- From: pat hayes <phayes@ihmc.us>
- Date: Mon, 19 Jan 2004 19:53:52 -0600
- To: "Jos De_Roo" <jos.deroo@agfa.com>
- Cc: Austin Tate <a.tate@ed.ac.uk>, public-sws-ig@w3.org
>PatH: >[...] >> BTW, the same abstraction works very well for space. Traditional >> spatial models start with points (where you click the digitizing pen >> on the map) then go to (oriented) line-segments (pair of points) then >> to end-linked sequences (paths) then to closed paths (end=beginning >> and no crossings) which define (oriented) 2-d regions. These all >> build up very nicely as finite structures on points. You can even go >> to 3-d and higher, using ideas from homology theory, by stitching >> together 2-d cells into 2-d surfaces and defining closure by >> cancellation of oriented edges. All of which suggests that this is >> indeed a very robust (and certainly very simple) framework. > >That sounds great Pat - can you recommend any URI pointers ?? >Thanks in advance :) Still no URI, but I found the relevant part of my paper copy of the 1997 USIGS Data Model. In sum, its basically this: Locations are described by Geometric-Spatial-Elements G-S-Es are Surfaces or Points or Lines or Volumes A Point in a Surface is a Surface-Point... <various subclassifications of surface types, eg fan-surface, etc.> Point is the locus of a Node Line is the locus of an Edge Surface may be covered by Faces .... <etc. relating actual topography items to topological idealizations> Now: Node, Edge, Ring, Face and Shell are all Topological-Elements, and they are related as follows: Node is identified by a Point (with coordinates) Edge has two Nodes (starting and ending) and may be a Ring-edge; Ring is composed of a Sequence of Ring-edges with a 'succeeding/preceding' relation on them; A Ring may be used as a Face-Ring, and may be Internal or External (only one external allowed); a Face is bounded by a Face-ring, and may itself be used as a Shell-face: and a Shell is composed of Shell-Faces. USIGS didn't get into the 3-d homology stuff, but you can get that from a topology textbook. Basic idea: treat each edge piece as having an orientation and say that opposite orientations cancel. Then add up all the edges of all the rings of all the shell-faces. If the result is zero, the shell (surface) is closed; if not, then there are holes in the surface and the surplus edges are the edges of the hole(s). For an example, orient four triangles clockwise, join their edges into a tetrahedron so that matching edges cancel. Now remove one of the four sides and do the edge arithmetic again. I bet there are algorithms based on this stuff built into the silicon hardware of an X-box these days. >-- >Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/ > >PS we some related work (roll algoritm) 25 years ago >but I guess that a lot has evolved since then... Nah, the stuff Im talking about goes back to about 1940. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ihmc.us http://www.ihmc.us/users/phayes
Received on Monday, 19 January 2004 20:53:55 UTC